Time to enquire about assignment (4)
I believe the answer is:
task
'assignment' is the definition.
(I've seen this in another clue)
'time to enquire' is the wordplay.
'time' becomes 't' (abbreviation).
'to enquire' becomes 'ask' (to enquire is to ask or question).
't'+'ask'='TASK'
'about' acts as a link.
(Other definitions for task that I've seen before include "Set piece of work" , "Burden with work" , "Errand, duty" , "Chore, job." , "exercise" .)